🔥 Thermodynamics – Stage 2

Page 9 : Carnot Engine & Absolute Temperature Scale

Carnot Engine defines the maximum possible efficiency of any heat engine. No real engine can cross this limit.

1️⃣ What is a Carnot Engine?

A Carnot engine is an ideal reversible heat engine operating between two heat reservoirs:

🔥 Hot reservoir at temperature T₁
❄ Cold reservoir at temperature T₂

✔ It gives the maximum efficiency possible between T₁ and T₂.

2️⃣ Carnot Cycle – Four Processes

(i) Isothermal Expansion (at T₁)
Heat absorbed Q₁ from hot reservoir

(ii) Adiabatic Expansion
Temperature drops from T₁ to T₂

(iii) Isothermal Compression (at T₂)
Heat rejected Q₂ to cold reservoir

(iv) Adiabatic Compression
Temperature rises from T₂ to T₁

3️⃣ Efficiency of Carnot Engine

Efficiency (η) = Work output / Heat absorbed

η_Carnot = 1 − (T₂ / T₁)

⚠ Temperatures must be in KELVIN

4️⃣ Key Conclusions from Carnot Theorem

No engine can be more efficient than a Carnot engine
All reversible engines between same T₁ and T₂ have same efficiency
Efficiency depends only on temperatures, not on working substance

5️⃣ Absolute Temperature Scale

Carnot efficiency expression led to the definition of absolute temperature.

Absolute zero is the temperature at which:
👉 Carnot efficiency becomes 100%

Absolute zero = 0 K = −273.15 °C

6️⃣ Why 100% Efficiency is Impossible?

For η = 1,
T₂ must be 0 K

❌ Absolute zero cannot be reached ❌ Hence 100% efficiency is impossible

7️⃣ JEE Advanced Traps

Using °C instead of K
Assuming efficiency depends on engine design
Thinking real engines can reach Carnot efficiency
Confusing Carnot engine with refrigerator

8️⃣ Ranker’s One-Line Memory

Carnot engine sets the upper limit
η depends only on T₁ and T₂
Kelvin scale is compulsory

✅ Stage 2 – Page 9 Completed
➡️ Next: Stage 2 – Page 10 : Entropy & Clausius Inequality

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Thermodynamics – Set 1
Set 2
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Set 5
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Set 7
Set 8
Set 9
Set 10
Set 11
Set 12
Set 13
Set 14
Set 15
Set 16
Set 17
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Set 23
Set 24
Set 25
Set 26
Set 27
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Set 30
Set 31
Set 32
Set 33
Set 34
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Set 37
Set 38
Set 39
Set 40
Set 41
Set 42
Set 43
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Set 45
Set 46
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